Sharp asymptotics for isotonic regression

The asymptotic behavior of the isotonic estimator of a monotone regression function (that is the least-squares estimator under monotonicity restriction) is investigated. In particular it is proved that the L-1-distance between the isotonic estimator and the true function is of magnitude n(-1/3). Moreover, it is proved that a centered version of this L-1-distance converges at the n(1/2) rate to a Gaussian variable with fixed variance.